I did not get this question at all, if someone could help, I would appreciate it!
It says:
Reword Theorem 1-3 as two statements, one describing existence and the other describing uniqueness.
Theorem 1-3 says:
If two lines intersect, then exactly one plane contains the lines.
Earlier in the lesson it explained something about existence (there is at least one point of intersection) and uniqueness (no more than one such point exists) about Theorem 1-1, but I still couldn't put the two together. Can anyone help??? I need this homework turned in tomorrow, or it's late. Any help is appreciated! THANKS!!!
To reword Theorem 1-3 as two separate statements, one describing existence and the other describing uniqueness, we need to consider what the theorem is saying.
The original statement of Theorem 1-3 says: "If two lines intersect, then exactly one plane contains the lines."
Let's break it down:
1. Existence: This part of the theorem deals with the existence of a solution. In the context of lines and planes, it means there is at least one plane that contains the given two lines when they intersect.
2. Uniqueness: This part of the theorem deals with the uniqueness of the solution. In the context of lines and planes, it means there cannot be more than one plane that contains the given two lines when they intersect.
Using these explanations, we can reword Theorem 1-3 as two separate statements:
Existence statement: If two lines intersect, there exists at least one plane that contains the lines.
Uniqueness statement: If two lines intersect, no more than one plane contains the lines.
To summarize, Theorem 1-3 states that when two lines intersect, there is at least one plane that contains them, and there cannot be more than one such plane.